Conventional analog microscopes and digital microscopes (even those with digital imaging cameras attached) are designed as they have been for the past few centuries to present images to the human eye using magnification (image size) as the primary parameter. Conventional microscopes use a combination of an objective lens and a viewing lens (either eyepiece or “tube-lens”) to send the image of an object at a desired magnification to the image (or focal) plane where it is imaged by the human eye or a digital imaging device. The lenses define the magnification. The theoretical best resolution of such an optical system can be computed but is rarely, if ever actually, in practice achieved. Employing digital imaging devices on conventional microscopes further compromises image resolution and contrast for magnification. This has always meant striking a balance between “blur”, contrast, and size. In other words, although modern digital imaging microscopes can make very good and “pleasing” images, they do not really achieve the best physically possible.
The Nyquist criterion or sampling theorem states that for a limited bandwidth (band-limited) signal with maximum frequency (fmax), an equally spaced sampling frequency (fs) must be greater than twice the maximum frequency (fmax), i.e., fs>=2 fmax in order to have the signal be uniquely reconstructed without aliasing. The frequency 2 fmax is called the Nyquist sampling rate. Half of this value, fmax, is sometimes called the Nyquist frequency. The sampling theorem is considered to have been articulated by Nyquist in 1928 and mathematically proven by Shannon in 1949.
The Nyquist criterion is being applied to design digital imaging systems. For example, in Nikon's MicroscopyU website, which provides an educational forum for various aspects of optical microscopy, digital imaging, and photomicrography, in a section titled “Digital Camera Resolution Requirements for Optical Microscopy” it is stated that “[a]dequate resolution of a specimen imaged with the optical elements of a microscope can only be achieved if at least two samples are made for each resolvable unit, although many investigators prefer three samples per resolvable unit to ensure sufficient sampling.” While Olympus' online Microscopy Resource Center echoes this statement in a section titled “Electronic Imaging Detectors.” In another section of the website titled “Spatial Resolution in Digital Images”, it is further stated that “[t]o ensure adequate sampling for high-resolution imaging, an interval of 2.5 to 3 samples for the smallest resolvable feature is suggested.”